Question 1 Consumption (30 points)

a)  Using the permanent income hypothesis in a two-period setting, derive the consumption for a representative agent that will receive a stimulus check from Joe Biden (SC) in the first period and pay back the same amount of the check in the second period (a new tax called the            payback tax, PbT). 10pts

Budget constraint for period 1: A1 - A0 = Y1 - T1 + rA0 - C1 + SC

Budget constraint for period 2: C2 = Y2 - T2 + (1+r)A1 - PbT                                                 C2 = Y2 - T2 + (1+r)[Y1 - T1 + (1+r)A0 - C1 + SC] – PbT                                                        C2 = -(1+r)C1 + Y2 - T2 + (1+r)[Y1 - T1 + (1+r)A0 + SC] – PbT                                             After we assume C1 = C2 = C: C = {Y2 - T2 + (1+r)[Y1 - T1 + (1+r)A0 + SC] – PbT}/(2+r)

b)  Will this stimulus check structure (subsidy in period 1 and tax in period 2, SC=PbT) increase or decrease consumption (in comparison with no subsidy and no payback tax)? 5pts

The alternative would lead to C = Y2 - T2 + (1+r)[Y1 - T1 + (1+r)A0 ]/(2+r). The stimulus check structure will increase consumption, since the stimulus check can be saved and provide returns of (1+r)SC, which is larger than PbT.

c)  How will the consumption choice change if the tax in period 2 is paid with interests ((1+r)PbT)? 10pts

C = {Y2 - T2 + (1+r)[Y1 - T1 + (1+r)A0 + SC] – (1+r)PbT}/(2+r). Since (1+r)SC = (1+r)PbT: C = [Y2 - T2 + (1+r)[Y1 - T1 + (1+r)A0]/(2+r).

In this case, the consumption choice will be the same as if there was no stimulus check and payback tax. This is a case of Ricardian Equivalence; the public policy does not affect real outcomes.

d)  As a policymaker, which of the two alternatives would you choose in order to stimulate the economy and end a recession? Are there any other factors other than Ricardian Equivalence to be considered? Explain. 5pts

In order to increase consumption and stimulate the economy, the payback tax cannot include interests. Other factors to consider include expectations, uncertainty, and political stability,  among others.

Question 2 Unemployment (20 points)

a)  According to the Mortensen-Pissarides Model and assuming that bargaining power is equal between employers and workers and that Vv=0, prove that  . 10pts

Value functions for worker:

Value functions for firms:

rVE = w − b(VE − VU )    &   rVU =  a(VE − VU )

rVF = (Y − w − C) − b(VF − VV )  &  rVV = −C + α(VF − VV )

Bargaining power is equal, then:   VE − VU = VF − VV,    VE − VU = VF

After substituting, we obtain:  , such that

b)  Who (employer or worker) keeps a higher share of the output when a>α? Explain 5pts

When a > α, workers can find job faster than firms can fill their vacancies, more than half of the output goes to worker.

c)   In the current economy, how can you explain the low unemployment and increased wages?

5pts

The current economy shows that workers have a higher bargaining power, a > α . Higher bargaining power allows workers to be pickier about the jobs they take and negotiate higher salaries.

Question 3 Inflation (20 points)

Consider an economy that behaves as in the Kydland and Prescott Model with the following Social Loss Function: L = 0.6(y – y*)2 + 0.4a(π – π*)2

a)  How would the Central Bank optimize inflation if they can anchor expectations (full credibility) and if they can’t anchor expectations? 10pts

1-  If expectations are anchored (full credibility): π = π*

2-  If expectations are not anchored: Min    0.6(yn + b(π − πe) – y*)2 + 0.4a(π – π*)2

1.2(yn + b(π − πe) – y*)b + 0.8a(π – π*) = 0

π(1.2b2 + 0.8a) = 0.8aπ* – 1.2(yn − bπe – y*)b

π = 1/(1.2b2 + 0.8a)  [0.8aπ* – 1.2(yn − bπe – y*)b]

π = 1/(1.2b2 + 0.8a)  [0.8aπ* + 1.2b(y*- yn) + 1.2b2πe + 1.2b2π*  - 1.2b2π*]

冗 = 冗* + 1/(1.2b2 + 0.8a) [1.2b(y*- yn) + 1.2b2冗e - 1.2b2冗*]

b)  What would the equilibrium inflation be if people don’t fully trust that the FED can keep inflation under control? 10pts

In equilibrium π = πe

πe = π* + 1/(1.2b2 + 0.8a)  [1.2b(y*- yn) +1.2b2πe - 1.2b2π*]

πe – 1.2b2πe/(1.2b2 + 0.8a)  = π* + 1/(1.2b2 + 0.8a)  [1.2b(y*- yn) - 1.2b2π*] πe [0.8a /(1.2b2 + 0.8a)] = π* + 1/(1.2b2 + 0.8a)  [1.2b(y*- yn) - 1.2b2π*]

πeq = πe = [(1.2b2 + 0.8a)/ 0.8a]π* + 1/ 0.8a [1.2b(y*- yn) - 1.2b2π*]= π*+1.2b(y*- yn)/0.8a

Question 4 Current Macroeconomic Topics (30 points)

a)  Explain the long-term repercussions of a government with a structural deficit and provide examples. What type of reforms does a government in this situation need to do? 10pts

Countries with structural deficits accumulate debt. The long-term repercussion is that debt is repaid with more debt, which elevates the accumulated debt and the risk of default. Paying more interests makes this debt more expensive to pay and forces to accumulate more of it, leading to a vicious cycle. Examples of countries include Costa Rica, which initially had a low structural deficit but after the Great Recession and COVID experienced a decrease in GDP and tax revenue, leading to an unsustainable debt. Another example happened in Europe after the formation of the EU. Countries that were used to use monetary policy for competitiveness and payment of government expenditures lost that capacity and started to accumulate debt. Finally, after the COVID recession, most countries experienced a decrease in GDP and tax revenue, building a larger structural deficit and debt accumulation. A long-term repercussion of this debt will be increased taxes in the future, lower stability, and a decrease of well-being. Government  reforms  to  stabilize  the  structural  deficit  include  tax  reform,  decrease  of government   expenditures,   renegotiation   of  debt,   targeted   loans   from   multilateral organizations, and coordination with regional central bank, among others.

b)  How is the COVID recession similar to the Great Recession? How is it different? 10pts

In both cases there was a slowdown of economic growth and an increase of the budget deficit. Both recessions led to an initial decrease in consumption and required fiscal policy (such as the ARRA, CARES, and American Rescue Plan) as well as expansionary monetary policy to keep the interest rates low. Both recessions are different from the causes, the Great Recession started after the burst of the housing market bubble, while the COVID recession originated from shutdowns and a decrease of overall consumption. Some fiscal policy actions and bailouts were different, targeting groups affected such as small business during COVID vs financial institutions during the Great Recession.